Chemical Equation Balancer
Balance any chemical equation exactly, then assign oxidation states by the standard priority rules, with worked examples for peroxides, OF2, and Fe3O4.
Balanced equation
Enter an equation
Exact rational nullspace solver, smallest integer coefficients.
| Side | Species | Coefficient |
|---|
Oxidation states
Enter a formula
Sum-rule average oxidation state per element.
| Element | Atoms | Oxidation state | Source rule |
|---|
composition matrix times coefficient vector equals zero
How?
How this is calculated
Each species is a column and each element is a row. Reactant atom counts are positive and product atom counts are negative. The solver computes reduced row echelon form exactly over rational numbers, classifies the nullspace, then scales the unique positive direction to the smallest integer coefficients.
Formula: composition matrix times coefficient vector equals zero
How to calculate oxidation state
An oxidation state is the charge an atom would carry if every bond went to the more electronegative partner. Assign one by four steps, and the "Oxidation states" mode above shows each step for the formula you enter.
- A free element is 0. O2, Fe, and S8 are all 0.
- The states over a species sum to its net charge, which is 0 for a neutral formula and the ion charge otherwise.
- Fix the elements that follow a rule, in priority order: F = -1, then group 1 = +1 and group 2 = +2, then H = +1 when a more electronegative atom is present and -1 (hydride) otherwise, then a lone halogen = -1, then O = -2, then a lone S = -2.
- Solve the remaining element from the sum. Fe3O4 gives O = -2 on 4 atoms, so the 3 iron atoms average +8/3, reported exactly rather than as +2.67.
The priority order settles the hard cases without a lookup table. In H2O2 an oxygen is present, so H stays +1 and O relaxes to -1. In OF2 fluorine is fixed at -1 first, so O relaxes to +2. Each row names the rule that set it, so a relaxed oxygen reads "relaxed, solved by sum", never "O = -2". "Oxidation state" and "oxidation number" are IUPAC synonyms for the same quantity.
Sources
- OpenStax Chemistry 2e, Writing and Balancing Chemical Equations. OpenStax. Retrieved .
- An Innovative Approach to Balancing Chemical-Reaction Equations. arXiv. Retrieved .
- IUPAC 2016 Recommendations: Comprehensive Definition of Oxidation State (Pure Appl. Chem. 88(8):831). IUPAC. Retrieved .
- IUPAC Gold Book, oxidation state (O04365). IUPAC. Retrieved .
- LibreTexts, Oxidation States (Oxidation Numbers). LibreTexts. Retrieved .
- OpenStax Chemistry 2e, Classifying Chemical Reactions (Oxidation-Reduction). OpenStax. Retrieved .
Method last reviewed